I am not sure exactly what "mish mash" you have in mind, but do not try to feed
a ferroresonant transformer with anything except a sine waive. Many/most cheap
UPS output square waves when running on the battery. I learned the hard way,
have blown 2 perfectly good UPSs that way.
A good sine wave inverter generator should run a CVT just fine, but why would
you want to? The inverter output should already be voltage regulated.
BTW: Ferroresonant transformers are power vampires. Just put your hand on one
after it has been on a while and estimate how many watts it is dissipating as
waste heat. I have one I have been known to use as a foot warmer!